Water reservoir

The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?

Result

a =  10 h
b =  15 h

Solution:

1a+1b=1s s=aba+b a=4+s b=9+s  a=4+aba+b b=9+aba+b  a2=4(a+b) b2=9(a+b)  a>0;b>0 a=10 b=15 s=6 \dfrac1a + \dfrac1b = \dfrac1s \ \\ s = \dfrac{ab}{a+b} \ \\ a = 4 +s \ \\ b = 9 + s \ \\ \ \\ a = 4 + \dfrac{ab}{a+b} \ \\ b = 9 + \dfrac{ab}{a+b} \ \\ \ \\ a^2 = 4(a+b) \ \\ b^2 = 9(a+b) \ \\ \ \\ a>0; b>0 \ \\ a = 10 \ \\ b = 15 \ \\ s = 6 \ \\

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